Municipal solid waste (MSW) incineration offers advantages such as volume reduction and resource recovery, making it widely used for urban waste disposal. However, the large amounts of incineration ash produced are often processed into recycled aggregates (RA) to replace sand in mortars and concrete. To ensure RA quality, fine particles are typically removed through water washing and drying, resulting in significant water and energy consumption. This study proposes a crushing-screening-granulation technique to convert municipal solid waste incineration ash (MSWIA) into recycled fine aggregates (RFA) and artificial coarse aggregates (ACA). The effects of MSWIA fine particles, mineral admixtures as partial cement substitutes, and the RFA-to-sand replacement ratio on mortar properties were examined. ACA was prepared under various curing conditions, and its particle strength was tested. High-strength RA concrete was produced using ACA and RFA. Results show that excessive MSWIA fine particles in RFA hinder cement hydration. Partial cement replacement with silica fume improves the mechanical properties of RA mortar. Increasing the RFA replacement ratio reduces mechanical properties and flowability but increases water retention. When curing ACA with cement and silica fume, bulk crushing strength reached 9.3 MPa. Concrete containing ACA showed 68% higher compressive strength and 57% higher flexural strength than RFA mortar. The dry separation of coarse ash particles combined with granulation significantly improves RA material properties and enhances ash utilization, achieving full resource recovery.